Finite Group Databasebeta

← C3×#63691 #11722355

Subgroups — C3×#63691 #11722355

Order 864.

145 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 145 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41⋊C9C211yesmaximal, characteristic, complemented
2C3×#3689C211yesmaximal, characteristic, complemented
3C3×#3688C211yesmaximal, characteristic, complemented
4C3×#950—31nomaximal
5#63691C311yesmaximal, characteristic, direct product factor
6C3×C4×D9—41nomaximal
7C3×Q8⋊C9C2211yescharacteristic
8C32×#41D311yescharacteristic
9C3×#235—31no—
10C3×#216—31no—
11C3×#215—31no—
12C3×#214—31no—
13C3×#213—31no—
14C2×C3×C3⋊C8—31no—
15#41⋊C9—21no—
16#41⋊C9C2×C311yescharacteristic, complemented
17#3689C2×C311yescharacteristic, complemented
18#3688C2×C311yescharacteristic, complemented
19C2×C3×D9—41no—
20C3×C4×C9—41no—
21C3×Dic9—41no—
22C3×#135—91no—
23#950—31no—
24C32×Q8C2×D311yescharacteristic
25C32×D4—31no—
26C2×C32×C4—31no—
27C3×#67—61no—
28C3×D12—31no—
29C3×C4×D3—61no—
30C3×Dic6—31no—
31C3×C3⋊C8—31no—
32C3×C3⋊C8—31no—
33C4×D9—41no—
34Q8⋊C9—21no—
35Q8⋊C9C22×C311yescharacteristic
36C2×C3×C9—41no—
37C3×D9—42no—
38C3×#41—21no—
39C3×#41—91no—
40C3×#41D911yescharacteristic, complemented
41C3×#41C3×D311yescharacteristic
42#235—31no—
43C3×Q16—91no—
44C3×SD16—91no—
45C3×SD16—91no—
46C3×D8—91no—
47C2×C3×C8—91no—
48#216—31no—
49#215—31no—
50#214—31no—
51#213—31no—
52C2×C3⋊C8—31no—
53C22×C32—31no—
54C2×C3×D3—61no—
55C32×C4—31no—
56C32×C4S411yescharacteristic
57C3×Dic3—61no—
58C2×D9—41no—
59C4×C9—41no—
60C4×C9—81no—
61Dic9—41no—
62#135—91noSylow
63C3×C9—41noSylow
64C3×Q8—21no—
65C3×Q8—91no—
66C3×Q8C2×D911yescharacteristic
67C3×Q8C2×C3×D311yescharacteristic
68C3×D4—31no—
69C3×D4—31no—
70C3×D4—61no—
71C3×D4—91no—
72C3×D4—181no—
73C2×C3×C4—31no—
74C2×C3×C4—31no—
75C2×C3×C4—61no—
76C2×C3×C4—181no—
77#67—61no—
78D12—31no—
79C4×D3—61no—
80Dic6—31no—
81C3×C8—91no—
82C3×C8—91no—
83C3⋊C8—31no—
84C3⋊C8—31no—
85C2×C32—61no—
86C2×C32C2×S411yescharacteristic
87C3×D3—121no—
88C2×C9—41no—
89C2×C9—81no—
90D9—42no—
91#41—91no—
92#41C3×D911yescharacteristic, complemented
93Q16—91no—
94SD16—91no—
95SD16—91no—
96D8—91no—
97C2×C8—91no—
98C22×C3—31no—
99C22×C3—31no—
100C22×C3—61no—
101C22×C3—181no—
102C2×D3—61no—
103C3×C4—21no—
104C3×C4—31no—
105C3×C4—31no—
106C3×C4—61no—
107C3×C4—181no—
108C3×C4(C22⋊C9)⋊C211yescharacteristic
109C3×C4C3×S411yescharacteristic
110Dic3—61no—
111C32#98511yescharacteristic
112C9—41no—
113C9—81no—
114Q8—91no—
115Q8C2×C3×D911yescharacteristic
116D4—31no—
117D4—91no—
118D4—181no—
119C2×C4—31no—
120C2×C4—181no—
121C8—91no—
122C8—91no—
123C2×C3—21no—
124C2×C3—61no—
125C2×C3—61no—
126C2×C3—121no—
127C2×C3—361no—
128C2×C3C2×(C22⋊C9)⋊C211yescharacteristic
129C2×C3C2×C3×S411yescharacteristic
130D3—121no—
131C22—31no—
132C22—181no—
133C4—31no—
134C4—181no—
135C4C3×(C22⋊C9)⋊C211yescharacteristic
136C3—21no—
137C3#6369111yescharacteristic, direct product factor
138C3C3×#98511yescharacteristic
139C2—61no—
140C2—361no—
141C2C2×C3×(C22⋊C9)⋊C211yescharacteristic
subgroupG/H
center, hypercenterC3×C4(C22⋊C9)⋊C2
commutator, cosocle, hypocenterQ8⋊C9C22×C3
FrattiniC2×C3C2×C3×S4
FittingC32×#41D3
socleC2×C32C2×S4
LCSG ▷ Q8⋊C9
UCSC1 ◁ C3×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#41⋊C9C2semidirect
2. C3×#3689C2semidirect
3. C3×#3688C2semidirect
5. #63691C3direct (N × H)
16. #41⋊C9C2×C3semidirect
17. #3689C2×C3semidirect
18. #3688C2×C3semidirect
40. C3×#41D9semidirect
92. #41C3×D9semidirect
137. C3#63691direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#41⋊C92
C3×#36892
C3×#36882
C3×#9503
#636913
C3×C4×D94